Image restoration by minimizing zero norm of wavelet frame coefficients

In this paper, we propose two algorithms, namely extrapolated proximal iterative hard thresholding (EPIHT) algorithm and EPIHT algorithm with line-search (EPIHT-LS), for solving `0 norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of KurdykaLojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of `0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.